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A ratio compares two quantities. It tells us how many times one quantity fits into another. For instance, if we say the ratio of apples to oranges is 3 to 2, it means for every 3 apples, there are 2 oranges. Ratios can be written in different ways:

• Using the colon symbol, like 3:2.
• Using the word 'to,' like 3 to 2.
• As a fraction, like 3/2.

Understanding ratios helps us understand proportions and relations between different quantities. Let's look at converting ratios into fractions.

Converting ratios into fractions is straightforward. The first number in the ratio becomes the numerator, and the second number becomes the denominator.
For example, in the ratio 5 to 7, the fraction form would be: ewline ewline \(\frac{5}{7}\).ewline
Remember, fractions show a part of a whole. So, when we convert a ratio to a fraction, we are expressing how much of one part is present compared to the whole.
Consider converting the ratio 329 to 967 from the exercise into a fraction. The fraction form is: ewline ewline \(\frac{329}{967}\). This fraction is not simplified, as simplifying is not always required. Understanding fraction conversion helps us see ratios in another form, making it easier to compare and work with.

In any fraction, the numerator and the denominator play crucial roles. The numerator is the top number, and it tells us how many parts we have. The denominator is the bottom number, and it tells us how many parts make up a whole.
For example, in the fraction \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator. This fraction means we have 3 parts out of a total of 4 equal parts.
Using the ratio from our exercise, 329 to 967 as a fraction \frac{329}{967}\, 329 is the numerator, and 967 is the denominator.
When working with fractions:

• Always place the numerator over the denominator.
• The denominator cannot be zero, as division by zero is undefined.
• Simplifying fractions involves dividing the numerator and denominator by their greatest common divisor (GCD).

Understanding numerators and denominators helps you work efficiently with fractions and ratios.